algebraic congruence

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• Congruence — is the state achieved by coming together, the state of agreement. The Latin congruō meaning “I meet together, I agree”. As an abstract term, congruence means similarity between objects. Congruence, as opposed to equivalence or approximation, is a …   Wikipedia

• Congruence lattice problem — In mathematics, the congruence lattice problem asks whether every algebraic distributive lattice is isomorphic to the congruence lattice of some other lattice. The problem was posed by Robert P. Dilworth, and for many years it was one of the most …   Wikipedia

• Congruence relation — See congruence (geometry) for the term as used in elementary geometry. In abstract algebra, a congruence relation (or simply congruence) is an equivalence relation on an algebraic structure (such as a group, ring, or vector space) that is… …   Wikipedia

• Congruence subgroup — In mathematics, a congruence subgroup of a matrix group with integer entries is a subgroup defined by congruence conditions on the entries. A very simple example would be invertible 2x2 integer matrices of determinant 1, such that the off… …   Wikipedia

• Algebraic geometry — This Togliatti surface is an algebraic surface of degree five. Algebraic geometry is a branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. It… …   Wikipedia

• Modulus (algebraic number theory) — In mathematics, in the field of algebraic number theory, a modulus (plural moduli) (or cycle,[1] or extended ideal[2]) is a formal product of places of a global field (i.e. an algebraic number field or a global function field). It is used to… …   Wikipedia

• Semigroup — This article is about the algebraic structure. For applications to differential equations, see C0 semigroup. In mathematics, a semigroup is an algebraic structure consisting of a set together with an associative binary operation. A semigroup… …   Wikipedia

• Leibniz operator — One of the cornerstone concepts in the theory of abstract algebraic logic is that of the Leibniz operator.MotivationThe Leibniz operator was introduced by Willem Blok and Don Pigozzi, two of the founders of the field, as a means to abstract the… …   Wikipedia

• mathematics — /math euh mat iks/, n. 1. (used with a sing. v.) the systematic treatment of magnitude, relationships between figures and forms, and relations between quantities expressed symbolically. 2. (used with a sing. or pl. v.) mathematical procedures,… …   Universalium

• Compact element — In the mathematical area of order theory, the compact or finite elements of a partially ordered set are those elements that cannot be subsumed by a supremum of any non empty directed set that does not already contain members above the compact… …   Wikipedia

• Kernel (algebra) — In the various branches of mathematics that fall under the heading of abstract algebra, the kernel of a homomorphism measures the degree to which the homomorphism fails to be injective. An important special case is the kernel of a matrix, also… …   Wikipedia